Appendix F: General Statistical Theory

2016 ◽  
pp. 503-521
Author(s):  
Karl G. Jöreskog ◽  
Ulf H. Olsson ◽  
Fan Y. Wallentin
Keyword(s):  
Statistical Theory ◽  
General Statistical

Indexed Text-Analysis

1974 ◽  
Vol 13 (03) ◽  
pp. 179-183 ◽  
Author(s):  
K. Kayser ◽  
W. W. Höpker ◽  
U. Müller
Keyword(s):  
Statistical Theory ◽  
Text Analysis ◽  
Formal Description ◽  
Total Entropy ◽  
Loss Of Information ◽  
Medical Text ◽  
Medical Terms ◽  
General Statistical ◽  
General Conditions

General conditions for medical text analysis are discussed. By means of formal description the errors which occur during manual codification with the over-cross method are analysed by distribution in different classes of diagnoses. It is pointed out that the largest error arises through incorrect correlation of the diagnoses in the summary of findings with those of the thesaurus and that, furthermore, a thesaurus of 4,500 medical terms is not sufficient for documentation in pathology. The entropy losses were only slightly larger than the losses of diagnoses calculated by percentage. The distribution of the classes of diagnoses follows a general statistical theory. In the over-cross method a loss of information Iμ = 1.532 in a total entropy of HD = 5.789 must be reckoned with as shown in an example.

Deductive Development of the Theory

2018 ◽  
Author(s):  
John von Neumann
Keyword(s):  
Statistical Theory ◽  
The State ◽  
Theory Building ◽  
Statistical Ensemble ◽  
Basic Assumptions ◽  
Definite Operator ◽  
General Statistical

This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ‎] (∥φ‎∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ‎] is the state φ‎).

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